1. Field of the Invention
The present invention relates to an optical apparatus of an image forming apparatus such as a laser printer or a copying machine, which radiates a laser beam onto an image carrier to form an image.
2. Description of the Related Art
In an image forming apparatus such as a copying machine or a printer, as an apparatus for forming an electrostatic latent image on a photosensitive drum, one using a laser beam is frequently used. In such an apparatus, a diverging laser beam emitted from a laser emission device such as a semiconductor laser propagates through a collimator lens and a prism compressor, and is converted to a collimated beam. The laser beam is then guided to a scanning mirror which rotates at high speed, so that its reflection direction is changed in accordance with rotation of the scanning mirror, and scans along the longitudinal direction (main scan direction) of the photosensitive drum. Thus, an electrostatic latent image is formed on the photosensitive drum.
In this apparatus, the laser emission device includes a single emission unit. For this reason, if an image forming speed is to be increased, it is restricted by a rotational speed of the scanning mirror and the like, and a remarkably high-speed image forming operation cannot be achieved.
For this reason, in recent years, an apparatus has been developed wherein the photosensitive drum is simultaneously scanned with a plurality of laser beams emitted from a plurality of light emission units. In this apparatus, first and second laser beams 8 and 10 emitted from laser emission device 6 having first and second light emission units 2 and 4 propagate through single collimator lens 12 to be converted to collimated beams. Laser beams 8 and 10 propagate through identical prism compressor 14, so that the widths of laser beams 8 and 10 in the sub-scan direction are compressed. Laser beams 8 and 10 are then radiated on scanning mirror 16. First and second laser beams 8 and 10 reflected by scanning mirror 16 are focused by first and second f-.theta. lenses 18 and 20, and are then guided toward photosensitive drum 22. Thus, first and second laser beams 8 and 10 are scanned in the longitudinal direction as the main scan direction on photosensitive drum 22. As a result, electrostatic latent images corresponding to the two laser beams are simultaneously formed. Thus, the image forming speed can be increased.
However, in this apparatus, a pitch between laser beam spots in the sub-scan direction perpendicular to the main scan direction on photosensitive drum 22 is normally several tens of micrometers, while a pitch between first and second light emission units 2 and 4 must be at least 100 micrometers in order to prevent a variation in output due to thermal interference therebetween.
For this reason, in this apparatus, laser emission device 6 is inclined at .theta..sub.B (deg) with respect to the sub-scan direction, as shown in FIG. 2, so that first and second laser beams 2 and 4 simultaneously scan on adjacent scanning lines on photosensitive drum 22. Therefore, in this apparatus, since laser emission device 6 is inclined, if first and second laser beams 8 and 10 are radiated on photosensitive drum 22 in this state, image A formed by a laser beam spot of first laser beam 8 is offset by .DELTA.l.sub.D from image B formed by the laser beam spot of second laser beam 10 in the main scan direction, as shown in FIG. 3. Even if an offset between two images A and B is reduced by electrical processing, image quality is considerably degraded, and sectional shapes of laser beams 8 and 10 on photosensitive drum 22 are inclined, resulting in further degraded image quality.
Image point distance .DELTA.l.sub.D as an offset between laser beams 8 and 10 in the main scan direction will be described in detail below.
The optical principle until laser beams 8 and 10 are radiated on photosensitive drum 22 in this apparatus will be described with reference to FIGS. 4 to 8. In FIGS. 4 and 5, light emission units 2 and 4 are arranged at a focal point of collimator lens 12 for collimating laser beams 8 and 10 into collimated beams. If a diffusion angle in the sub-scan direction of laser beam 8 or 10 in light emission unit 2 or 4 is represented by .theta..sub..omega.F (deg), and its diffusion angle in the main scan direction is represented by .theta..sub..omega.S (deg), beam radius .omega..sub.F (mm) in the sub-scan direction and beam radius .omega..sub.S (mm) in the main scan direction in collimator lens 12 are: EQU .omega..sub.F =F.sub.C .times.tan .theta..sub..omega..sbsb.F, .omega..sub.S =F.sub.C .times.tan .theta..sub..omega..sbsb.S ( 1)
(where F.sub.C is the focal length of collimator lens 12) If an inclination of a beam center in the sub-scan direction when the beam is output from collimator lens 12 is represented by .theta..sub.2F (deg) and an inclination of the beam center in the main scan direction is represented by .theta..sub.2S (deg), the following relations are established: ##EQU1## (where l.sub.B is the distance between first and second light emission units 2 and 4, and .theta..sub.B is the angle defined between a line connecting first and second light emitting units 2 and 4 and the sub-scan direction) Thereafter, if the radii of laser beams 8 and 10 in the sub-scan direction are multiplied with .alpha. by prism compressor 14, since the angle between two main beam components of laser beams 8 and 10 becomes 1/.alpha., beam radius .omega..sub.MF (mm) in the sub-scan direction and beam radius .omega..sub.MS (mm) in the main scan direction in scanning mirror 16 are: EQU .omega..sub.MF =.alpha..omega..sub.F =.alpha.F.sub.C .times.tan .theta..sub..omega.F ( 4) EQU .omega..sub.MS =.omega..sub.S =F.sub.C .times.tan .theta..sub..omega.S ( 5)
Distance h.sub.MF (mm) of laser beams 8 and 10 from the optical axis in the sub-scan direction and distance h.sub.MS (mm) thereof from the optical axis in the main scan direction are given by: EQU h.sub.MF .apprxeq.l.sub.2 .times.tan .theta..sub.2F +l.sub.3 .times.tan (.theta..sub.2F /.alpha.) (6) EQU h.sub.MS .apprxeq.(l.sub.2 +l.sub.3).times.tan .theta..sub.2S ( 7)
(where l.sub.2 (mm) is the distance from an image-side focal point of collimator lens 12 to the exit of prism compressor 14, and l.sub.3 is the distance from the light output side of prism compressor 14 to scanning mirror 16)
The optical principle while the laser beams reach photosensitive drum 22 from scanning mirror 16 will be described with reference to FIG. 6. In FIG. 6, reference numeral 24 denotes an imaginary equivalent lens having composite focal length F.sub.1 equivalent to a synthesized one of first and second f-.theta. lenses 18 and 20. In order to correct surface oscillation on each mirror surface of scanning mirror 16, the following relation is established over the entire length of photosensitive drum 22 in the longitudinal direction: EQU 1/d+1/e=1/F.sub.1 ( 8)
(where d (mm) is the optical path length from scanning mirror 16 to equivalent lens 24 in the sub-scan direction, and e (mm) is the optical path length from equivalent lens 24 to photosensitive drum 22 in the sub-scan direction) Under this condition, if a distance of laser beam 8 or 10 from the optical axis in the sub-scan direction on photosensitive drum 22 is represented by h.sub.dF (mm), the following relation is established: EQU h.sub.dF /h.sub.MF =e/d=.beta. (9)
(where .beta. is the absolute value of the lateral magnification of equivalent lens 24)
Therefore, as shown in FIG. 3, when adjacent 0.085-mm wide scanning lines are simultaneously scanned without forming an interval between first and second laser beams 8 and 10 in the sub-scan direction, the following relation must be established: EQU .beta..times..theta..sub.MF =h.sub.dF =P.sub.2 /2 (10)
(where P.sub.2 is the pitch in the sub scan direction) For example, if d=842.762 mm, e=123.987 mm, and F.sub.1 =108.085 mm, .beta..apprxeq.0.14712 from equation (9). Since P.sub.2= 0.085 mm, from equations (4) and (10), .beta..omega..sub.MF =.beta..alpha.F.sub.C =tan .theta..sub..omega.F =P.sub.2 /2=0.085/2, and hence, .omega..sub.MF =0.085/(2.times.0.14712).apprxeq.0.29 mm. If .alpha.=1/5 and tan .theta..sub..omega.F =0.15, F.sub.C =0.085/(2.beta..alpha..times.tan.theta..sub..omega.F).apprxeq.0.629 mm.
From equations (6), (9), and (10), ##EQU2##
Meanwhile, if l.sub.B =0.1 mm, tan .theta..sub.2F =(0.1.times.cos .theta..sub.B)/(2.times.9.629)=5.1926.times.10.sup.-3 cos .theta..sub.B from equation (2). Therefore, if l.sub.2 =10 mm and l.sub.3 =10 mm,
From equation (11), ##EQU3##
If focal length f of f-.theta. characteristics in the main scan direction is given by f=210 (mm), images are offset by .DELTA.l.sub.D =F.times..theta..sub.2S =210.times.1.9373.times.10.sup.-2 .apprxeq.0.407 (mm) as image point distance .DELTA.l.sub.D of laser beams 8 and 10 in the main scan direction.
In this apparatus, the offset of the images formed by first and second laser beams 8 and 10 on photosensitive drum 22 due to inclination of laser emission device 6 is corrected as follows. More specifically, as shown in FIG. 1, the starting portion of the beam reflected by horizontal sync reflection mirror 26 is detected by horizontal sync detection pin diode 28. This detection signal is supplied to a sync signal detector (not shown). When the sync signal detector sends a sync signal to a controller (not shown), the controller delays an information signal of second laser beam 10 from an information signal of first laser beam 8 by a predetermined period of time by a shift register with reference to the sync signal, thereby correcting the image offset. The delay time by the shift register is set by an operator while observing a printed image.
In this apparatus, the following approximate expressions are also established based on FIG. 7: ##EQU4## (where .DELTA..theta. is the angle between the optical axis 34 and the main beam reflected from scanning mirror 16, which is influenced by the plane inclination of scanning mirror 16) ##EQU5##
On the other hand, the following approximate expression is established based on FIG. 8. More specifically, from equations (6) and (9). EQU h.sub.dF =.beta.h.sub.MF =.beta.(l.sub.2 .times.tan .theta..sub.2F +l.sub.3 .times.tan(.theta..sub.2F /.alpha.) (15)
However, l.sub.3 is varied depending on the radiation position on scanning mirror 16, and the variation is given by: EQU .DELTA.l.sub.3 .apprxeq.(R.sub.1 -R.sub.2)/cos .theta..sub.REF ( 16)
(where R.sub.1 is the radius of a circumcircle of scanning mirror 16, R.sub.2 is the radius of an inscribed circle of scanning mirror 16, .theta..sub.REF is the angle defined between a line connecting center 30 of scanning mirror 16 and radiation position 32 of laser beam 8 or 10 and laser beam 8 or 10)
Therefore, ##EQU6##
In this apparatus, first f-.theta. lens 18 has focal length f, and focuses laser beams 8 and 10 on photosensitive drum 22 in the main scan direction, so that distance l.sub.M from an intersection between optical axis 34 and drum 22 on drum 22 in the main scan direction is given by l.sub.M =f.theta..sub.M when laser beams 8 and 10 are scanned at angle .theta..sub.M with respect to optical axis 34 of first and second f-.theta.lenses 18 and 20. Meanwhile, second f-.theta. lens 20 corrects oscillation of laser beams 8 and 10 in the sub-scan direction caused by surface oscillation of each surface of scanning mirror 16, and focuses laser beams 8 and 10 in the sub-scan direction.
Therefore, focusing of laser beams 8 and 10 in the sub-scan direction is performed mainly by second f-.theta. lens 20 only. For this reason, the heights of laser beams 8 and 10 at second f-.theta. lens 20 are large, and as a result, incident angles of laser beams 8 and 10 from second f-.theta. lens 20 to photosensitive drum 22 are increased. For this reason, if a distance from second f-.theta. lens 20 to photosensitive drum 22 varies, laser beams 8 and 10 are largely offset on photosensitive drum 22 in the sub-scan direction. As a result, image quality is considerably degraded.